An Estimable Model of Supermarket Behavior: Prices, Distribution Services and Some Effects

of Competition*

Roger R. Betancourt and Margaret Malanoski Economics Department Office of Information and Regulatory Affairs U. of Maryland Office of Management and Budget College Park, MD 20742 Washington, DC Ph: 301 4053479 Fax:301 4053542 Revised January 1999

Abstract In this paper we present and estimate a simple model of supermarket behavior that has several attractive properties: It permits the incorporation of the (distribution) services provided by a supermarket as an output of supermarkets and a determinant of demand for supermarket products; it generates, as a special case, one of its main competitors in the supermarket literature -- the so called full price model of services; and, it can be estimated with a unique data set originally constructed by the Economic Research Service of USDA. The main results of the analysis are three. First, the aggregate demand for a supermarket=s products depends critically on distribution services: at the substantive level, a 1 % increase in these services increase quantity demanded by 0.4%; at the methodological level, the restrictions on the parameter values implied by the model are critical in the evaluation of functional forms for demand. Second, supermarkets exhibit constant marginal costs with respect to the quantity of output or turnover and substantially declining marginal costs with respect to (distribution) services, which implies substantial multiproduct economies of scale. Third, in response to an exogenous increase in competition those supermarkets that have adopted newer formats such as superstores and that employ newer technology such as optical scanners choose prices and (distribution ) services in ways that increase consumer welfare, whereas those that do not have these characteristics choose prices and services in ways that lower consumer welfare. JEL Classification: L81, L1, L4. Key Words: Supermarkets, prices, distribution services, demand; economies of scale.

I. Introduction.

2

Supermarkets are an important component of modern economies. For

instance, according to the U.S. Statistical Abstract (1998), in 1996 the

retail trade accounted for 9.37% of U.S. GDP and supermarket sales

accounted for 12.3 % of sales in the retail trade. At the same time the

supermarket category has undergone major structural changes in the 1980's,

for example according to the U.S. Statistical Abstract (1991) the share of

sales of conventional supermarkets went from 73.1% in 1980 to 42% in 1989.

Newer formats gained the ground lost by conventional supermarkets. These

formats provide either broader and/or deeper assortments (for example

superstores, combination food and drug and hypermarkets), or in the case of

warehouses lower prices in exchange for less assurance of product delivery

in the desired form (large packages rather than small ones). By 1996, the

share of conventional supermarkets had fallen to 22.2%, U.S. Statistical

Abstract (1998).

In the trade literature the importance of the services provided by

supermarkets is frequently mentioned. For instance in a 1987 survey of

customers reported by The Progressive Grocer , prices were only one of 16

items considered important by half of the sample in selecting a food store.

The others were services of various kinds such as availability of a produce

department, unit pricing, convenient location, cleanliness, short waits at

checkout counters, etc. Similar results appear in other years, see for

example the April issue in 1993. By and large this aspect of supermarkets

has been either ignored or tangentially acknowledged in the mainstream

economics literature, including the industrial organization literature.

3

The major aim of this paper is to capture the importance of these

services as an economic variable that determines supermarket behavior both

theoretically and empirically. We will do so by treating them explicitly

as an output of supermarkets and as a determinant of consumers= demand for

supermarket products. In Section II, we present a simple theoretical model

that adapts the one in Betancourt and Gautschi (1993) for empirical

implementation with the data available to us. We show how this model

generates as special cases the standard textbook monopoly model, a model of

retail pricing proposed by Bliss (1988), and the perfectly competitive

model referred to as the full price model of services. The latter was put

forth by Ehrlich and Fisher (1982) to analyze the demand for advertising

and has been applied to supermarkets by Oi (1992) and to retailing in

general by Divankar and Ratchford (1995). Our simple model can be viewed

as a slight generalization of the Bertrand model that implies supermarkets

behave as imperfect competitors.

What makes this project feasible is a unique data set put together by

the Economic Research Service of USDA, see Kaufman and Handy(1989).

Supermarkets often provide over a 100,000 products and it is not easy to

obtain an average price charged by a supermarket; they also offer a variety

of services and it is not easy to obtain information on them. By combining

price surveys with a store survey, this data set allows the construction

for each supermarket of an index of prices and an index of services. The

latter correspond to the ones identified as distribution services in the

retailing literature from which the model is derived. Since this data was

4

also combined with social and economic information at the zip code level,

it becomes possible to estimate an aggregate demand function for each

supermarket that incorporates price and distribution services as endogenous

variables and that must satisfy certain theoretical restrictions implied by

the model. The results of this estimation are reported in Section III.

They show that distribution services are an important determinant of the

demand for supermarket products and that not all functional forms for the

demand functions satisfy the restrictions implied by the theory.

From the simple model one can extract the first-order conditions that

determine the choice of prices and distribution services by a supermarket.

By imposing functional forms on cost functions and on the limited

characterization of competition in the model, it becomes possible to

estimate these first-order conditions given the aggregate demand for the

supermarket products. These functional forms and their implications for

estimation are discussed in Section IV. Of particular interest is allowing

for the possibilities of increasing returns to scale, since this issue is

controversial in the literature. Some authors argue in favor of their

existence, Oi(1992) and Ofer (1973); other authors argue in favor of

constant returns to scale, Ingene (1984) and Cotterill(1991). We find that

both groups are right. That is we find constant returns to scale with

respect to turnover or the standard output measure but increasing returns

to scale with respect to distribution services or the output measure we are

emphasizing here.

5

The last section of the paper presents the results, discusses various

econometric issues and reports a simulation: namely, the effect of a

change in the exogenously given level of competition for each observation

(supermarket) using the estimated parameter values. The simulation results

are interesting for two reasons. First, they confirm the main criticisms

of the traditional linear regressions of prices against measures of market

power in grocery retailing made by Anderson (1990). He argues that a

change in competition may not have the same effect on prices in all markets

and we find that prices sometime increase and sometimes decrease; he also

argues that it is necessary to control for differences in quality (what we

call distribution services) and we find that these services also sometimes

increase and sometimes decrease. Second, we find that our sample splits

along interesting characteristics in their response to a change in

competition. For instance supermarkets where consumer welfare increases

have a higher proportion of superstores and use of optical scanners than

those where welfare decreases, which suggests the structural changes we

have observed in the 1980's have been beneficial to consumers.

II. The Model and Its Main Special Cases.

The essence of the model is that retailers choose prices and

distribution services simultaneously given the demand function for

supermarket products and the level of competition in the market. Formally,

we write the constrained maximand for a supermarket as

L = pQ - C(v, Q, D) - wQ +µN[E=- E(p, p=, D, z0 )]

6

where p is a store=s average retail price; Q is the level of output, which

is determined by the aggregate demand faced by the store. N is the number

of transactions. We will assume that all repeated purchases are the same

and that all consumers of any one supermarket are identical; hence, Q= qN,

where q is the demand function per transaction of the representative

consumer, and N will be normalized at unity. C is a neoclassical cost

function describing the costs of supermarket activities as a function of

input prices (v) and the two outputs of this retailing activity, explicit

products and services (Q) and the implicit levels of distribution services

(D). w is the average price of the explicit products and services

purchased from suppliers. E is the expenditure function of the

representative consumer, which depends on the store=s average retail price

(p), the distribution services of the supermarket (D), other prices ( p=)

faced by the consumer and the optimal level of the consumption activities,

z0.1 E= is the lowest cost to this 'representative consumer' of attaining

her maximum level of utility at an alternative establishment. µ is a

Lagrange multiplier.

Since this constrained maximand is unfamiliar to many economists, it

is instructive to discuss what it captures explicitly. The first three

terms are the standard definition of profits for a retail establishment, in

which it is useful to separate sales (pQ) and two dimensions of costs:

those due to the distribution activities of the retailer ( C(v, Q, D)) and

those due to the production activities of wholesalers or suppliers (wQ).

The fourth term represents a constraint that captures the effects of

7

competition on supermarket behavior in the following sense. If there is a

lowering of the competitive standard that a store faces, for example by a 1

$ increase in the lowest cost per transaction to a 'representative

consumer' of attaining her maximum level of utility at an alternative

establishment, the Lagrange multiplier, µ, measures the marginal

contribution to profits of such an experiment. µ ranges between zero and

unity.2 This constraint captures Bliss (1988) concept of retail

competition as offering the consumer better value for her money than at the

next best alternative store in terms of an expenditure function that allows

for the existence of distribution services and makes explicit the

assumption of identical transactions across consumers and repeat

purchases.3

Optimal choices of prices and services by a supermarket must satisfy

Price: (p - CQ - w)(MQ/Mp) + Q(1-

µ) = 0 (1)

Distribution Services: (p - CQ -w)(MQ/MD) +µr - CD = 0

(2)

Constraint: E= - E(p, p=, D, z0 )

= 0 (3).

It is insightful to proceed by considering several special cases that

this model generates, which can be seen through these conditions. Suppose

we assume first that µ= 0. The constraint becomes irrelevant and we have

a generalization of the standard monopoly case in the literature. (1) and

8

(2) simply imply that the retailer chooses prices and distribution services

such that marginal revenues equal marginal costs in both cases.

Suppose we assume instead that µ= 1. Condition (1) implies p = CQ +

w, or the average retail price equals the marginal cost of retailing an

additional unit of output plus the cost of purchasing this unit from

suppliers; condition (2) implies that r = CD, or the shadow price of an

additional unit of distribution services to the representative consumer

equals the marginal cost of providing this additional unit to the consumer.

Thus, we have a generalization of standard competitive behavior in a model

that incorporates distribution services as a variable. Notice that in this

model the conjectural variation is zero. That is the supermarket takes its

rivals prices and distribution services as given.4 Hence, this model has

all the advantages and disadvantages of the Bertrand model as discussed,

for example, in Tirole (1988, Ch. 5). In particular, the slightest

departure from competitive behavior results in the supermarket losing all

of its sales to the representative consumer. This helps interpret the more

general model. Namely, when 0 < µ < 1, the supermarket loses a fraction

of its sales to the representative consumer when it fails to meet the

competitive standard represented by the constraint.

By making an additional assumption in this special case when µ = 1,

it is possible to generate the full price model of services. Ehrlich and

Fisher (1982) argued that perfect competition implies that the full price

paid by the consumer must be the same at every store. Retailers can

compete by offering whatever combination of services and prices they want

9

as long as they meet this constraint. The full price in our model is the

sum of the retail price and the shadow price of distribution services, p +

r. The implication of Ehrlich and Fisher=s argument is that this sum is

equal to a constant, let us say K, which must be the same for every store.

From equation (1) and (2) when µ= 1, this also implies that p + r = K = CQ

+w + CD . The second equality brings out a little known feature of the

full price model. Namely if there are decreasing marginal costs with

respect to distribution services (information in Ehrlich and Fisher=s

case), for example, the model breaks down. That is, given K, increases in

p and decreases in r imply that CQ decreases (if marginal costs are

increasing with respect to output or turnover, Q) and CD decreases (if

marginal costs are decreasing with respect to distribution services, D) and

the second equality can not be met.

III. Specification and Estimation of the Aggregate Demand Function for a

Supermarket.

Implementing the previous model empirically requires estimation of

the aggregate demand function for a supermarket. In this section we

specify and estimate this aggregate demand function, taking into account

the restrictions implied by the previous model. Equation (4) below

specifies the aggregate demand function for a supermarket,

Q = g(p, D, Y, X)u3 . (4).

Q is the level of demand, which is measured as the annual level of sales of

the store deflated by the store=s average price. u3 is a disturbance term,

which is assumed to be lognormally distributed so that lnu3 is normally

10

distributed with E(lnu3 ) = 0. We follow the applied literature by

specifying g in ACobb-Douglas@ form so that it generates elasticities as

parameters and a 'double log' type of demand function5 , i.e.,

lnQ = α + δ1 lnp + δ2 lnD +δ3 lnY +δ4 lnX +ln u3.

(5)

One modification of (5) is useful in an empirical setting because it

allows us to take advantage of one of the strengths of our data, which

permit the representative consumer faced by a supermarket to differ across

supermarkets. Namely, the elasticities affecting the endogenous variables,

p and D, need not be assumed constant. Instead, they will be allowed to

vary with characteristics of the households in the zip code area in which a

supermarket is located, that is

δ1 = δ10 +δ11 X1 < -1 (6)

0 # δ2 = δ20 +δ21 X2 < 1. (7)

Economic theory leads us to expect a negative price response and a

positive distribution services response. Thus, we would expect δ10 < 0 and

δ20 > 0 . The signs of δ11 and δ21, however, would be determined by whether

we expect the household characteristic to increase or decrease the

sensitivity of demand to retail prices or distribution services,

respectively. In the empirical analysis we will assume X1 to be the

percentage of households without cars in the zip code area where a

supermarket is located; hence, we would expect it to decrease the absolute

value of the price elasticity of demand, so that we would expect δ11 >0

because the lesser the access to a car of the representative consumer the

11

less price elastic is demand. This allows us to investigate empirically

one of the mechanisms by which supermarkets may charge different prices to

poor households. We will assume X2 to be the socioeconomic status of the

zip code area where the supermarket is located.6 The inequalities in (6)

and (7) have to be satisfied or second-order conditions in the model of

Section 2 would be violated. This provides a test of the empirical

judgements made, including the selection of X1 and X2 . Y was measured as

the median income in the zip code area where the supermarket was located

and δ3 is, of course, expected to be positive.

X was specified as a vector of three exogenous variables: a dummy

variable indicating whether or not the store was in a shopping center (X41

),7 the population of the zip code area where the store was located (X42 )

and the selling area of the supermarket measured in squared feet of store

space devoted to selling (X43 ). Selling area captures the consequences of

an estimate of the level of demand made by those who designed the

supermarket and unobserved by the researcher and it should be positively

related to the level of demand. Population should be positively related to

the level of demand facing the supermarket if everything else in the zip

code area were equal. Finally, the dummy controls for one of the things

that may not be equal: namely, the pattern of store traffic may be

different when a store is located in a shopping center so that it may have

a higher or lower level of demand given population and selling area.

The Economic Research Service (ERS) of USDA has developed a unique

data base which is the basis for our analysis. It consists of three price

12

surveys (waves 1,2,3) taken six weeks apart in 1982; a separate survey of

store characteristics undertaken over the same period; demographic and

socioeconomic information for zip code areas purchased by ERS from Claritas

Corporation; and SMSA data. We gathered data on the number of food stores

in each SMSA. A detailed description of the data is provided in an

Appendix available upon request.

The data is essentially cross-section data with the unusual feature

that for one variable there are three observations or drawings. That is,

each of the three price surveys generated a store price index, p. Not all

the stores were the same in each price survey, so we worked with a sample

of 430 observations that were included in each wave and checked our results

against the wider samples. The annual sales of each store and the price

index were used to generate Q for each wave. The store characteristics

survey generated the data to construct an index of distribution services

for each store, D, based on the response to twenty questions about whether

or not the store provided a particular service. In addition, for the

estimation of demand the variables X41 and X43 were taken from the store

survey while X1, X2, Y, and X42 were taken from the Claritas data set.

Descriptive statistics on these variables as well as on those introduced in

the next section are presented in Table 1.

>>>>>Table 1 GOES HERE>>>>>>

Table 2 presents the results of estimating (5) with the modifications

implied by (6) and (7) for each of the three waves. The equation to be

estimated is linear in the parameters but nonlinear in the endogenous

13

variables (p and D); hence, it was estimated by nonlinear two stage least

squares.8 The results are not very sensitive to the price survey used in

the analysis. In all three cases, inequalities (6) and (7) are satisfied

without violations at any data point. The coefficients of price,

distribution services, the interaction between price and percentage of

households without a car, median income and selling area have the expected

sign and are statistically significant at well beyond the 1% level in all

three price surveys. The coefficients of population and the shopping

center dummy are not statistically significant at the 2.5% and at the 5%

level, respectively, in any of the three waves. Finally, the interaction

between distribution services and socioeconomic status is statistically

significant at the 5% level in waves 1 and 2 and at the 10% level in wave

3.

>>>>>Table 2 GOES HERE>>>>

Our results show that it is feasible empirically to incorporate

distribution services into the estimation of demand functions for

supermaket products in a theoretically consistent fashion. Substantively, a

1% increase in store price decreases quantity demanded by about 2.0 to 2.2

% on average and a 1% increase in store distribution services increases

quantity demanded by about 0.38 to 0.42% on average. In addition, we find

that one of the mechanisms through which the poor face higher prices is

that their price elasticity of demand is smaller (in absolute value) when

they reside in households without a car. Not surprisingly, establishments

built to sell more do so, but not proportionately ( the hypothesis that the

14

coefficient is unity is rejected at the 1% level); on the other hand,

households with a higher level of median income buy proportionally more at

the supermarket. Higher socioeconomic status in an area reduces the

magnitude of the increase in demand from increasing distribution services,

perhaps because households in these areas take for granted a high level of

distribution services.

In the course of our analysis we performed a number of experiments,

some of which are worth reporting. We set the interaction terms to zero

(δ11 = δ21 =0). The estimated price elasticity was negative and

statistically significant at the 5% level, but less than unity in absolute

value which violates second-order conditions. We also estimated our

specification with SMSA dummies added. The price elasticity estimate was

negative but the null hypothesis that it was greater than or equal to minus

unity could not be rejected at any reasonable level of significance. We

estimated the specification with (not shown) and without an intercept (

Table 2). The intercept estimate is quite large and statistically

insignificant (t < 1), and the null hypothesis that the coefficient of

distribution services is greater than or equal to unity can not be rejected

at any reasonable level of significance for two of the waves and at the 1%

level for all three waves. All three alternatives were discarded because

of their inconsistency with the theoretical restrictions emanating from the

simple model of Section II.

IV. Specification of the First- Order Conditions.

15

Because the model presented in Section II is a perfect information

one, we introduce error terms in equations (1) and (2), u1 and u2

respectively, by assuming that the source of the errors is in the

application of the decision rules for optimization by each agent

(supermarket), not in their perceptions of the objective function. These

considerations lead to the following set of equations for estimation.9

Price: (p - CQ -w) (MQ/ Mp)

+Q (1-µ) = u1 (8)

Distribution Services: (p - CQ - w)(MQ/MD) + µr - CD

= u2 (9).

We will assume E(ui ) = 0, and E(u1u2 ) … 0. That is, the errors in the two

equations capturing the decisions of a supermarket with respect to prices

and distribution services are likely to be correlated and will be allowed

to be in the estimation.10

In order to estimate (8) and (9), we need to specify the marginal

costs with respect to Q and D and the (exogenous) level of competition

faced by a supermarket (µ). Since Q depends on the endogenous variables,

p and D, it will be treated as an endogenous variable in the estimation of

(8) and (9). While equations (8) and (9) have the same form for every

supermarket, their values vary across supermarkets because aggregate

demand, the slopes of the demand functions, marginal costs and the level of

competition can vary across supermarkets. The disturbance terms will be

assumed to be independent and identically distributed across supermarkets.

16

In order to proceed, we need to specify functional forms for the

marginal cost functions for explicit products, CQ, and distribution

services, CD. Our choice was guided by several considerations. First,

the strength of our data is in the measurement of the two aggregate outputs

of supermarkets, Q and D. Second, whether marginal costs are increasing or

decreasing in these outputs is an important consideration in the full price

model, as shown in Section II, but the logic extends to the more general

model. Finally, as noted in the introduction, the issue of whether or not

there are returns to scale in retailing, including supermarkets, has

attracted considerable attention in the literature. Of the multiproduct

cost functions suggested in the standard reference in the industrial

organization literature for multiproduct cost functions, Baumol, Panzar and

Willig (1982, Ch. 15), the one that seemed most suitable in light of these

considerations is a slight generalization of the quadratic cost function

attributed to Braunstein by Baumol and Braunstein (1977).

It generates the following marginal cost functions,

CQ = (exp(θS))[α1 + α11 β Q(β

- 1) + α12 D][v1

π(1) v2 π(2) ]

(10)

CD = (exp(θS))[α2 + α22 λD(λ - 1) + α12 Q][v1

π(1) v2 π(2) ]

(11)

where v1 is occupancy cost, constructed on the basis of SMSA data, and v2

is labor compensation, which was measured in terms of an index of within

SMSA=s variations for each store.11 S is a vector of shift variables that

lead to differences in the levels of costs, for example store type (S1 is a

17

dummy for superstores and S2 is a dummy for traditional supermarkets with

warehouses as the residual category) or the existence of a scanner at the

store (S3). θ is a vector of corresponding coefficients. These four

variables were taken from the store survey.

This specification generalizes the standard quadratic form. That is,

if β = 2 = λ, it collapses to the quadratic. It allows for richer

behavior in terms of multiproduct returns to scale and the shape of

marginal costs than permitted by the standard quadratic.12 For instance,

with these functions marginal costs can increase at either an increasing or

a decreasing rate with distribution services or output as λ or β is

greater or less than one, respectively. Moreover the standard definition

of multiproduct returns to scale as the proportionate increase in costs as

a result of a proportionate increase in outputs, RTS, yields in this case

RTS = 1 + [(β -1)α11 Q + (λ - 1)α22 D]/C.

(12)

Thus, we can easily identify whether returns to scale, if any, are being

generated by a decreasing marginal cost function with respect to

distribution services or with respect to output.

Finally, a data limitation imposes the need to estimate a component

of cost, namely the wholesale price. The latter was assumed to be a

function of whether or not the supermarket belonged to a chain as follows :

w = σ0 + σ1S4, where S4 takes on the value of unity if the store reported

belonging to a chain in the store survey and zero otherwise. σ0 is expected

18

to be positive and σ1 is expected to be negative, i.e., one of the benefits

of belonging to a chain is to secure products at advantageous prices. One

way of checking the reasonableness of this procedure is to check whether or

not the estimated margin, p- CQ - w, for any observation is negative, which

would violate second-order conditions. Fortunately, our data and

estimation procedures allow us to perform this check.

Just as indicated in Section II, the Lagrange multiplier (µ) captures

the level of competition faced by a supermarket as the fraction of sales to

the representative consumer diverted to other stores from a failure to meet

the competitive standard. Hence, one would expect it to vary across the

market areas13 where the supermarkets are located as characteristics of

these market areas differ. Thus, while the value of µ faced by any

supermarket is assumed constant, the value this constant takes on is

allowed to differ across supermarkets. In addition, the value that µ can

take on for any supermarket must lie between zero and unity. These

considerations were incorporated into the empirical analysis by specifying

the following logistic functional form

µ = eγM /(1 + eγM ),

(13)

where M is a vector of variables describing the characteristics of the

market area.14

One characteristic of a market area is market growth, which will be

measured as the rate of growth of food store sales over the previous five

years (M3 ). We would expect that a market area with high market growth,

19

given the same number of stores for example, would have a lower value of

µ than one with low market growth. That is the fraction of sales to the

representative consumer of any one supermarket diverted to other stores as

a result of failing to meet the competitive standard would be less in the

market area with high growth, which implies γ3 < 0 since Mµ/ MMj = γj µ(1 -

µ).

Two other variables were used in the vector M. The number of food

stores per 1000 persons in the SMSA where the supermarket is located, M2 .

One would expect that the higher this number, given market growth for

example, the higher the fraction of sales to the representative consumer of

anyone supermarket in the area that can be diverted to other stores as a

result of a failure to meet the competitive standard, i.e., γ2 > 0.

Finally, the last variable included in this vector was the market share of

the firm that owns the store in the SMSA where the store is located, M1 .15

Statistically, this variable is appealing because, in contrast to the

previous two, it varies across supermarkets within an SMSA as well as

across SMSA=s. Its economic interpretation, however, is complex. A high

market share by a firm in an SMSA can be an indicator of ability to

differentiate its offerings and, thus, lowers competition (γ1 < 0); on the

other hand, it can also be an indicator of dominance by a firm with a

competitive fringe, which increases competition (γ1 > 0). While our model

says nothing about how the level of competition in a market area is

determined, Ansari, Economides and Ghosh (1994) develop a model in which

either outcome can arise in equilibrium depending on the nature of consumer

20

preferences over attributes. When preferences are nonuniform, the second

outcome is more likely to arise.

Imposing all these functional forms on (8) and (9), we have

[p-{exp(θS)[α1 + α11 βQ(β -1) + α12 D][v1 π(1) v2

π(2) ]} - (σ0 + σ1S4 )] [δ1 ( Q/p )

]

+ Q (1 /(1 + eγM )) = u1

(8)=

[p-{exp(θS)[α1 + α11 βQ(β -1) + α12 D][v1 π(1) v2

π(2) ]} - (σ0 + σ1S4 )] [δ2 (Q/D) ]

+ ( eγM /(1 + eγM ))(r0 + r1 t) - {exp(θS)[α2 + α22 λD(λ -1) + α12 Q][v1 π(1) v2

π(2)

]} = u2 (9)=,

where the only new term is (r0 + r1 t). That is, we have replaced the

shadow price of distribution services, r, by a linear function of the

opportunity cost of time, t , which was measured by the between SMSA

variation in the index of labor compensation.16

V. Results.

Estimation by nonlinear two stage or three stage least squares

requires specifying an instrument matrix. We included every variable

treated as exogenous in the model as an instrument, which gave rise to 16

variables in the instrument matrix, and is similar to what would be done in

the linear case. In the nonlinear case, however, the use of squares of the

original variables and interaction terms improves the efficiency of the

estimates, by making the nonlinear approximations more accurate, although

if carried to an extreme, adding as many variables as one has observations

for example, it can lead to inconsistent estimates.17 We selected six

21

variables that vary both within and across SMSA=s and introduced their

squares as instruments.18 In addition, we introduced a variable not used

earlier and its square as instruments: the percentage of families with two

or more earners in the zip code area where each supermarket was located.

Finally, we added interaction terms between selling area and the other six

variables mentioned in this paragraph and between the percentage of

households with more than two earners and the remaining five variables. To

conclude we used the same 35 instruments, when the squares and interaction

terms are included, in the estimation of the demand equation and the first-

order conditions.19

In Table 3 we present the results of estimating (8)= and (9)= by

nonlinear three stage least squares for each of the waves. Our most

statistically robust results are for the parameter estimates associated

with the two output variables in the cost function. The substantive

implications of these parameter estimates also represent the most important

results of our estimation. The estimates of λ and β suggest that

economies of scale with respect to distribution services and not with

respect to output are the main source of increasing returns to scale for

supermarkets. The null hypothesis that marginal costs with respect to

output (Q) are constant can not be rejected at the 1% level of significance

in any of the three waves, although the point estimate indicates slightly

declining marginal costs. On the other hand the null hypothesis that

marginal costs are constant with respect to distribution services (D) is

rejected at the 1% level of significance and above for all three waves in

22

favor of the alternative that marginal costs are declining. These results

are also consistent with the literature cited in the introduction.20

Finally, a higher level of turnover (Q) increases the marginal costs of

providing a given level of distribution services (D) and viceversa.

>>>>>>Table 3 GOES HERE>>>>>>>>

Our estimates of the shadow price of distribution services are

statistically significant at the 1% level and above for every wave. If for

simplicity we evaluate the estimates at t=0, they imply that the value over

a year to all the consumers of a supermarket of a one unit increase in the

distribution services index varies between $22,100 and 27,800 across the

waves.21 To put this number in perspective note that this represents

between 0.32% and 0.33% of average supermarket sales in the sample, which

were close to 7 million in 1982$. The construction of our index of

distribution services implies that a one unit increase in the index at the

sample mean corresponds to an 11% increase in any of the 20 components

making up the index, i.e., the average value from adding the 20 services ,

which is 11.2357, divided by the average value of the index, which is

101.40. Adding a whole service category implies increasing the

distribution services index by 9, which implies a value to consumers

between 2.88% and 2.97 % of sales.22

With respect to the competition variables, market share and market

growth are statistically significant at the 1% level or above in all three

waves but the number of stores per 1000 persons is not statistically

significant at this level. The coefficient of market growth suggests that

23

the ability to retain patronage by supermarkets is substantially greater in

areas where demand is increasing very rapidly. The coefficient of market

share, on the other hand, suggests that an increase in the market share of

a firm in a market area lowers its ability to retain patronage, perhaps due

to increased competition from the fringe. This effect, however, is much

smaller in magnitude than the effect of market growth.

Of the shift parameters in the cost function, the presence of

scanners generates the most stable results. It is statistically

significant at the 1% level in all three waves and their presence implies a

lowering of costs between 2 and 3 %. The differences in costs between

traditional stores and warehouses are not statistically significant at any

reasonable level, but the differences in costs between warehouses and

superstores are at the 2.5 % level in waves 2 and 3. They imply that

superstores experience between 5 and 6 % higher levels of costs than

warehouses. Of the input parameters, the coefficient of occupancy cost is

positive and statistically significant at the 2.5% level but the

coefficient of labor costs while positive is not statistically significant

at any reasonable level.

Finally, our attempt to compensate for the lack of data on the cost

of goods sold was successful in the following sense. The estimated value

of σ0 is positive and statistically significant at the 2.5% level in waves

1 and 2 and belonging to a chain systematically lowers the costs of

acquiring goods in all three waves. Perhaps more importantly, the bottom

of the table shows that using these estimates there are no violations of

24

second-order conditions at any data points in waves 2 and 3 and only 1

violation in wave 1. The estimated value of the price cost margin index at

the sample mean varies between 23 and 26 index units across the waves.

Expressed relative to the store price index, (p - CQ -w)/p, it also

implies a margin between 23% and 26% of sales.23

We performed two experiments that tested alternative specifications

of competition in the model. Namely, we reestimated the model assuming

first that µ = 0 and subsequently that µ = 1, i.e., the extreme cases of

monopoly and perfectly competitive behavior. In neither case were we able

to obtain convergence, which suggests that imposing these assumptions leads

to a misspecified model. In contrast to these specification tests, we also

performed other specification tests that did not substantially affect any

of the results reported in Tables 2 and 3.24

We also considered an econometric issue especially relevant to our

context. Moulton (1990) argues that cross-section estimates of the effects

of aggregate variables , for example our SMSA variables, on micro units,

the stores in our sample, will be biased if there is spatial correlation.

We took the estimated residuals from (8)= and (9)= and calculated for each

SMSA the test statistic developed by Anselin and Kelejian (1997) for the

case of endogenous regressors with no spatially lagged dependent variables.

This statistic (TS) is defined as

TS = {[v= W v ]/ s2 ]/ tr (WW + W=W=), where v is a an Nx1 vector of

residuals from an equation for an SMSA with N observations; s2 is the

sample variance of the residuals from an equation within an SMSA; W is the

25

spatial weighting matrix, which in our case takes the form of an NxN matrix

with zeros in the diagonal and ones= in the offdiagonal elements. TS has a

χ2 distribution with one degree of freedom. The null hypothesis of zero

spatial correlation could not be rejected at the 1 % level for any of the

28 SMSA=s in either of the two equations.

Finally, we used the estimated model to explore the effects of an

increase in competition, either through a 1 % increase in the price

elasticity of demand (in absolute value terms) or a 1% increase in µ.

We solved the model for p and D for each observation using the values of

our parameter estimates. We augmented the coefficient values as indicated

above and solved the model again for p and D for each observation. This

allowed us to calculate the change in price and the change in distribution

services. We were also able to evaluate these changes in terms of monetary

units. That is, r∆D - ∆pQ (= V) is a money metric utility measure of the

change in consumer welfare. This is especially valuable when changes in p

an D occur in the same direction, because assessing welfare implications

requires an evaluation in terms of monetary units which is provided by V.

Two conclusions emerged from this experiment. First, different

supermarkets respond in different ways to these changes. Some change

prices and distribution services in the same direction, indeed they can

both increase or decrease; some in opposite directions. Second, the four

characteristics (statistically significant at the 5% level) differentiating

the sample of supermarkets where consumer welfare increased (V>0) from

26

those where it decreased (V<0) were a larger turnover (Q), a larger market

share in the SMSA for the firm owning the supermarket, a higher proportion

of superstores and a higher presence of scanners. Hence, these results

suggest that recent trends toward the adoption of superstore formats and

optical scanners are welfare improving for supermarket costumers when

there is an increase in either intratype competition or general competition

for the consumer=s dollar.

Notes

27

* Earlier versions of this paper were presented at the AEA Meetings in Washington, DC,

and at the third conference on Retailing and Services in the Gold Coast, Australia. Seminar

presentations were given at U. of Miami, U. of Maryland, U. of Vienna and the Social Science

Research Center in Berlin (WZB). We would like to thank without incriminating the following

individuals: James MacDonald, Walter Oi, I. Prucha, H. Kelejian, A. Sen, R. Kranton, L. Locay

and N. Wallace. Part of the research for this paper was undertaken while Betancourt was an IRIS

Fellow.

1. E is a restricted expenditure or cost function in that D plays the

role of a fixed input in this function. It has the well known implication (

Shephard=s Lemma) that ME/Mp = q(p, D, p=, z0). This is the Hicksian demand

function which upon substitution of the demand for the commodities, z0 =

g(p, p=, D,Y), generates the Marshallian demand function. See Deaton and

Muellbauer (1980, Chs. 2 and 10) for the general procedure or Betancourt

and Gautschi (1992) for its application to retail demand. In particular

the last reference shows that, if we assume that other prices faced by the

representative consumer (p=) are constant, the Marshallian demand can be

written as q(p, D, Y) and it will be decreasing in price (p), and

increasing in distribution services (D) and the consumer=s full income (Y).

Finally, just as any restricted cost or expenditure function, it has the

property that ME/MD < 0. And, this property can be used to define the

shadow price of distribution services, r = - ME/MD, or how much the

28

consumer would be willing to pay for an additional unit of distribution

services if it were available in the market at an explicit price.

2. If in the above example µ equals zero, we have the case of a

monopolist and there are no gains from meeting the competitive standard.

If µ equals unity the supermarket gains all the business of the

representative consumer. For values between zero and unity the supermarket

gains a fraction of the business of the representative consumer. If µ

exceeds unity second-order conditions are violated. Thus the maximum value

of µ is unity.

3. Incidentally µ captures intratype competition from other supermarkets. General competition

for the consumer=s dollar is captured in the price elasticity of demand. Unless otherwise stated

competition will refer to the former and not the latter.

4. Tirole (1988, p.244) notes that this is the only consistent

conjecture in a static model.

5. For applications of variants of this function to the demand for

supermarket products see Bode (1990).

6. There is a certain amount of judgement in what variables one selects

as X1 and X2 . The first variable suggested itself pretty easily in

light of arguments that the poor pay more at

supermarkets, MacDonald and Nelson (1991). There is no prior literature to

guide the choice of the second one, or to provide expectations about

29

its sign; hence, we chose an indicator of well- being with

independent variation that was not going to be used elsewhere in the

analysis.

7. The latter should be viewed as introduced in exponential form in (4), e.g., as eδX .

8. The list of instruments is the same as used in Section 5 and it will be discussed there.

9. In the equations below the constraint in (3) is not present. Since

the source of the errors is in the application of the decision rules not in

the objective function, the constraint is assumed to hold with certainty.

Note that it is not directly observable or estimable by the

econometrician.

10. The slopes of the demand function in (8) and (9) can be expressed in

terms of elasticities as (MQ/Mp) = δ1 (Q/p) and (MQ/MD) = δ2 ( Q/D), where

δ1 and δ2 correspond to the price elasticity of demand and the distribution

services elasticity of demand estimated in the previous section,

respectively.

11. See the data appendix for additional details.

12. We also considered a different functional form for the cost function,

namely the one employed by Pulley and Braunstein (1984). This function is

the standard quadratic with interaction terms between input prices and

outputs added to allow for heterotheticity. The results deteriorated and

we abandoned experimentation with alternative functional forms.

30

13. In our empirical work the market area was defined as the SMSA in

which the supermarket was located.

14. The variables in the vector M can be thought of as capturing

variations in E=, the minimum expenditure at alternative establishments,

across supermarkets in different market areas.

15. We also considered the SMSA=s four firm concentration ratio and four

firm Herfindhal index. Since these variables, just like the previous two,

take on the same values for each supermarket in an SMSA, they only vary

over the 28 different SMSA=s and this limited variation resulted in severe

multicollinearity problems.

16. Setting r1 to zero made no difference to the substantive results

reported in Section V.

17. See Kelejian and Oates (1981, Ch. 8) for an elementary but insightful

discussion of this issue and Amemiya(1985) for an advanced treatment.

18. Namely the index of labor compensation, the selling area of the

supermarket and four variables available for the zip code area where each

supermarket was located: the percentage of households without cars,

socioeconomic status, median income and population.

19. We checked the sensitivity of our results to the choice of

instruments. For instance, we dropped the interaction terms between the

percentage of households with more than two earners and the six other

31

variables and reestimated the demand equation and the first-order

conditions with the reduced set of 29 instruments. No substantive

statement made about the coefficient estimates in Section III or in this

section would be altered by using these results instead of those based on

the 35 instruments.

20. For instance, Ofer (1973) measured output as value added and argued

that, under certain assumptions, it is a perfect measure of the

(distribution) services provided by a store, D; he found evidence of

increasing returns to scale. On the other hand, Ingene (1984) measured

output as sales per establishment and argued that, under certain

assumptions, it was a perfect measure of turnover or explicit output, Q; he

found evidence of constant returns to scale.

21. Sales were measured in hundred of 1982$. Thus, we multiplied the estimate by 100.

22. Parenthetically, Messinger and Narasinham (1997) have estimated the

average value of one-stop shopping at supermarkets to be between 2.24% and

2.37 % of sales.

23. The average retail margin for food stores in 1982, according to the

Census of Retail Trade, was about 22%. Our numbers, however, are estimates

of the price-cost margin and our cost variables do not account for any

equipment costs.

24. For instance, we changed the values of α1 and α2 from 1 to .5 and

32

1.5 and reestimated the model for all three waves with these new values.

Also, we added the excluded observations from each wave and reestimated the

demand function and the first-order conditions.

References

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Anselin, L. and Kelejian, H.(1997) ATesting for Spatial Error Autocorrelation in the Presence of

Endogenous Regressors.@International Regional Science Review 20, 153-82.

Anderson, K.B. (1990) "A Review of Structure Performance Studies in Grocery Retailing."

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Ansari, A., Economides, N. and Ghosh, A. (1994) "Competitive Positioning in Markets with

Nonuniform Preferences." Marketing Science 13, 248-273.

Baumol, W. and Braunstein,Y.(1977) AEmpirical Study of Scale Economies and Production

Complementarities: The Case of Journal Publication.@ Journal of Political Economy 85,

1037-48.

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., Panzar, J. and Willig, R. (1982) Contestable Markets and the Theory of Industry

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Betancourt, R. and Gautschi, D. (1992) "The Demand for Retail Products and the Household

Production Model: New Views on Complementarity and Substitutability." Journal of

Economic Behavior and Organization 17, 257-75.

.(1993) "Two Essential Characteristics of Retail Markets and Their Economic

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Bliss, C.(1988) "A Theory of Retail Pricing." Journal of Industrial Economics 36, 372-91.

Bode, B. (1990) Studies in Retail Pricing. Ph. D. Thesis. Erasmus University.

Cotterill, R.W. (1991)"A Response to the Federal Trade Commission/Anderson Critique of

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Marketing Policy Report No. 13.

Deaton, A. and Muellbauer, J.(1980) Economics and Consumer Behavior. London:Cambridge

University Press.

Divakar, S. and Ratchford, B. (1995) "Estimating the Supply and Demand for Retail Services."

mimeo, SUNY at Buffalo.

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Ehrlich, I. and Fisher, L.(1982) AThe Derived Demand for Advertising: A Theoretical and

Empirical Investigation.@American Economic Review 72, 366-88.

Ingene, C. (1984) AScale Economies in American Retailing: A Cross-Industry Comparison.@

Journal of Macromarketing 4, 49-63.

Kaufman, P. R. and Handy, C. R.(1989) "Supermarket Prices and Price Differences: City, Firm,

and Store-Level Determinants." Economic Research Service, U.S. Department of

Agriculture, Technical Bulletin No.1776.

Kelejian, H. and Oates, W.(1981) Introduction to Econometrics: Principles and Applications.

New York: Harper & Row Publishers.

MacDonald, J. M. and Nelson, Jr., P. E.(1991) "Do the Poor Still Pay More? Food Price

Variations in Large Metropolitan Areas." Journal of Urban Economics 30, 344-59.

Messinger, P. and Narasimhan, C.(1997) "A Model of Retail Formats Based on Consumers

Economizing on Shopping Time." Marketing Science 16, 1-23.

Moulton, B. R.(1990) AAn Illustration of a Pitfall in Estimating the Effects of Aggregate

Variables on Micro Units.@ Review of Economics and Statistics 72, 334-38.

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35

Oi, W. (1992) "Productivity in the Distributive Trades: The Shopper and the Economies of

Massed Reserves." in Z. Griliches (ed.) Output Measurement in the Service Sector.

Chicago, IL: University of Chicago Press.

Progressive Grocer. (1987; 1993, April).

Pulley, L. B. and Braunstein, Y. M. (1984) "Scope and Scale Augmenting Technological Change:

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DC.: Department of Commerce.

TABLE 1: DESCRIPTIVE STATISTICS

VARIABLE

MEAN

STD. ERROR

MINIMUM

MAXIMUM

Price wave 1

99.24

5.71

66.36

118.85

Price wave 2

99.66

5.42

73.72

120.92

36

Price wave 3

99.82

5.83

68.76

135.27

Output1 wave 1

704. 47

528.42

52.86

3836.48

Output1 wave 2

702.64

534.47

51.62

3811.87

Output1 wave 3

699.98

528.74

51.66

3772.14

dist. services2

101.40

24.75

8.90

160.20

% wo cars

12.29

13.48

0.

90.

Socec. stat. idx.

54.20

11.23

30.

99.

Median Income

19082.65

6013.86

5901.

51175.

Sh. center dum.

0.6186

0.4863

0.

1.

Population

31586.72

17034.07

189.

93751.

Selling area

18397.20

11234.71

3000.

68381.

Occ. Cost

100.95

23.62

63.70

167.37

Lab. cost3

98.90

23.94

13.54

163.50

Superstore du.

0.1674

0.3738

0.

1.

Traditional du.

0.7883

0.4089

0.

1.

Scanner du.

0.2465

0.4315

0.

1.

Chain dummy

.6140

.4874

0.

1.

Market sh.

0.0801

0.0848

0.0001

0.4661

37

# sts.(per 000's)

0.9792

0.2094

0.6483

1.7838

Market growth

0.0082

0.0425

-0.0900

0.1060

opp. cost4

-0.280

21.28

-37.50

54.66

1 We constructed the output indexes by taking annual store sales in hundred=s of $1982 and dividing by the store

price index.

2 We constructed the distribution services index. Its main difference from the services index constructed by ERS is

the elimination of one of the twenty services categories (scanners, which is an input not an output) and the addition

of another available elsewhere in the original data (extended hours, which is an output); see the Data Appendix for

details.

3 Within SMSA labor cost.

4 Between SMSA labor cost

38

TABLE 2: NONLINEAR TWO STAGE LEAST SQUARES - [DEMAND EQUATIONS]

WAVE 1

WAVE 2

WAVE 3

PARAMETER

ESTIMATE

STD

ERROR1

ESTIMATE

STD

ERROR1

ESTIMATE

STD

ERROR1

δ10 price

-2.1336*

.4496

-2.2276*

.4525

-2.0194*

.4229

δ11 price *

hh wo cars

.0039*

.0006

.0040*

.0006

.0038*

.0006

39

δ20

services

.5016*

.1677

.5221*

.1586

.4639*

.1567

δ21 serv.*

socec. sta.

-.0017*

.0008

-.0019*

.0009

-.0015**

.0008

δ41

shopping

center

-.0433

.0508

-.0450

.0505

-.0403

.0508

δ3 median

income

.9336*

.1829

.9708*

.1733

.8842*

.1705

δ42

population

.0535**

.0316

.0553**

.0315

.0568**

.0316

δ43 selling

area

.8592*

.0504

.8583*

.0483

.8703*

.0481

R2

.515

.536

.525

δ1 MEAN

-2.0856

-2.1785

-1.9727

40

MINIMUM

-2.1335

-2.2276

-2.0194

MAXIMUM

-1.7825

-1.8676

-1.6774

δ2 MEAN

.4094

.4192

.3827

MINIMUM

.3332

.3340

.3154

MAXIMUM

.4505

.4651

.4189

1 White robust standard errors. * |t|>1.96. **�|t|>1.645.

41

TABLE 3: NONLINEAR THREE STAGE LEAST SQUARES -FIRST-ORDER CONDITIONS1

Wave 1

Wave 2

Wave 3

Parameter

Estimate

Std Error2

Estimate

Std Error2

Estimate

Std Error2

θ1 super

-.0385

.0496

.0100

.0364

.0240

.0287

θ2 trad.

.0162

.0465

.0459

.0357

.0584*

.0188

SHIFT

PARAMETERS IN

COST FUNCTION

θ3 scan.

-.0263**

.0152

-0.212*

.0107

-.0178**

.0099

INPUT

π1 occu.

.0720*

.0315

.0606*

.0239

.0524*

.0227

PARAMETERS

π2 lab.

.0271

.0206

.0209

.0188

.0220

.1860

α11

21.16*

8.380

36.76*

13.93

35.81*

14.08

β turno.

.9701*

.0373

.9577*

.0274

.9834*

.0190

42

α22

1633.90

1021.33

1217.76**

722.17

1087.49*

538.372

γ serv.

.4567*

.1359

.5393*

.1393

.5819*

.1251

α12

.0692*

.0153

.0684*

.0133

.0686*

.0131

σ0

35.34*

10.70

25.15**

15.05

17.92

15.72

WHOLESALE

PRICE

PARAMETERS σ1 chain

-1.6044*

.6732

-1.0385*

.5293

-1.5991*

.6010

γ1 sh.

.5140*

.2111

.4716*

.2272

.4182**

.2450

γ2 # st.

-.1154**

.0674

.0141

.0896

.0876

.0790

COMPETITION

PARAMETERS γ3 m.gr.

-1.6642*

.5888

-1.7869*

.6429

-1.6101*

.6170

r0

220.51*

62.95

250.98*

76.40

278.16*

84.27

SHADOW PRICE

PARAMETERS r1 time

.1873**

.0994

.1996*

.0988

.1817**

.0981

Mean

25.98

23.03

25.04

Minimum

-9.73

4.74

5.65

Maximum

52.75

51.24

60.22

p - CQ - w

Obs.<0

1

0

0

1 These estimates were obtained given values of unity for α1 and α2 and using the estimates of δ1 and δ2

for each

wave presented in Table 2.

2 White robust standard errors. * |t| >1.96. ** |t| > 1.645.

43